Question: On the first 6 quizzes of her chemistry class, Emily got an average score of 81. What does she need on the next quiz to have an overall average of 83?
Answer: Let her score on the next quiz be $x$ The sum of all of her scores is then $6 \cdot 81 + x$ The same sum must also be equal to $7 \cdot 83$ Solve: $x = 7 \cdot 83 - 6 \cdot 81 = 95$.